Question

The proportion of drivers who use seat belts depends factors such as age (young people are more likely to go unbelted) and sex (women are more likely to use belts). It also depends on local law. In New York City, police can stop a driver who is not belted. In Boston at the time of the survey, police could cite a driver for not wearing a seat belt only if the driver had been stopped for some other violation. Here are data from observing random samples of female Hispanic drivers in these two cities.

City	Drivers	Belted
New York	213	175
Boston	115	73

Comparing local laws suggests the hypothesis that a smaller proportion of drivers wear seat belts in Boston than in New York. Do the data give good evidence that this is true for female Hispanic drivers? (Use α = 0.05. Round your test statistic to two decimal places and your P-value to four decimal places.)

H0:	pNY (=  <  >  ≠) pB
Ha:	pNY (<  ≠  >  =) pB
z =
P-value =

CHOOSE ONE OF THE FOUR SYMBOLS IN THE PARENTHESIS

Answer 1

Given that,

For New York : n1 = 213, x1 = 175 and

For Bostan : n2 = 115, x2 = 73 and

Pooled proportion is,

The null and alternative hypotheses are,

H0 : pNY = pB

Ha : pNY > pB

This hypothesis test is a right-tailed test.

Test statistic is,

=> Z = 3.76

p-value = P(Z > 3.76) = 1 - P(Z < 3.76) = 1 - 0.9999 = 0.0001

=> p-value = 0.0001

Since, p-value is less than 0.05 level of significance, we reject the null hypothesis (H0).